Difference between revisions of "Parametrization"
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The most common parametrization is for a circle centered at the origin in the ''xy''-plane: | The most common parametrization is for a circle centered at the origin in the ''xy''-plane: | ||
| − | :<math>x=r \cos t</math> | + | *:<math>x=r \cos(t)</math> |
| − | :<math>y=r \sin t</math> | + | |
| − | :<math>z=0</math> | + | *:<math>y=r \sin(t)</math> |
| − | :<math>0 | + | |
| + | *:<math>z=0</math> | ||
| + | |||
| + | *:<math>0 \le t \le \pi</math> | ||
Always remember to be precise in determining the new limits on the new parameter ''t''. | Always remember to be precise in determining the new limits on the new parameter ''t''. | ||
Revision as of 21:43, January 13, 2010
Parametrization is a technique in calculus for expressing multiple variables in terms of only one variable, which is usually depicted as "t", over a specified range.
The most common parametrization is for a circle centered at the origin in the xy-plane:
- <math>x=r \cos(t)</math>
- <math>y=r \sin(t)</math>
- <math>z=0</math>
- <math>0 \le t \le \pi</math>
Always remember to be precise in determining the new limits on the new parameter t.
This technique is particularly useful for calculating extrema and line integrals.